Answer
$(-\infty,\infty)$.
Work Step by Step
Given $f(x)=\frac{1}{2x^2-x+7}$, we have $2x^2-x+7=2(x^2-\frac{1}{2}x+\frac{1}{16})-\frac{1}{8}+7=2(x-\frac{1}{4})^2-\frac{1}{8}+7\gt0$, thus we can find its domain as $(-\infty,\infty)$.
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
013421742X
ISBN 13:
978-0-13421-742-0
Chapter 4 - Inverse, Exponential, and Logarithmic Functions - Summary Exercises on Functions: Domains and Defining Equations - Exercises - Page 486: 13
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